A large part of the recent growth in wealth — in some economies nearly all of it — consists of rising property values, according to Thomas Piketty’s analysis.
What's the use of "... — .... — ..."?
A man named Thomas Piketty studied wealth.
He discovered that wealth has increased recently.
And that a major part of that increase came from an increase in the value of property.
In some countries that major part was almost all.
The text between the dashes is called an aside, extra information that is only loosely connected grammatically to the rest of the sentence.
Another way to look at the sentence is:
A large part of the recent growth in wealth consists of rising property values, according to Thomas Piketty’s analysis. In some countries nearly all of the recent grown in wealth consists of rising property.
Basically what the dashes did was to add in extra information about how much of wealth was from recent growth in different countries.